Q 9. - Calculus

Question

Write each of the inequalities in interval notation:

$\left|\left(x^2-1\right)+3\right|<0.5$

Step-by-Step Solution

Answer

No solution

Step 1. Given information

An inequality is $\left|\left(x^2-1\right)+3\right|<0.5$

Step 2. Explanation

$\begin{array}{rcl}\left|\left(x^2-1\right)+3\right|& <& 0.5\\ -0.5& <& x^2-1+3<0.5\end{array}$

Here,

$x^2-1+3>0.5$ is true for all width="10" style="max-width: none; vertical-align: -4px;" $x$ and $x^2-1+3<0.5$ is not true for any value of $x$

So, the given inequality has no solution.